Forecasters have warned that rivers in some places would continue to rise for days.
Day after day of heavy rain pounded the central US, rapidly swelling waterways prompted a series of flash-flood emergencies in from Texas to Ohio.
The National Weather Service said dozens of locations in multiple states were expected to reach major flood stage, with extensive flooding of structures, roads, bridges and other critical infrastructure possible.
At least 16 weather-related deaths have been reported since the start of the storms, including 10 in Tennessee.
A 57-year-old man died on Friday evening after getting out of a car that washed off a road in West Plains, Missouri.
Flooding killed two people in Kentucky — a nine-year-old boy swept away that same day on his way to school, and a 74-year-old whose body was found Saturday inside a fully submerged vehicle in Nelson County, authorities said.
Also on Saturday a five-year-old died at a home in Little Rock, Arkansas, in a weather-related incident, according to police. No details were immediately provided.
Tornadoes earlier in the week destroyed entire neighbourhoods and were responsible for at least seven of the deaths.
And interstate commerce is affected — the extreme flooding across a corridor that includes the major cargo hubs in Louisville, Kentucky and Memphis could lead to shipping and supply chain delays, said Jonathan Porter, chief meteorologist at AccuWeather.
The outburst comes at a time when nearly half of NWS forecast offices have 20 per cent vacancy rates after Trump administration job cuts — twice that of just a decade ago.
Louisville Mayor Craig Greenberg said the Ohio River rose about 1.5 metres in 24 hours and would continue to swell for days.
"We expect this to be one of the top 10 flooding events in Louisville history," he said.
Flash-flood emergency and tornado warnings continued to be issued across Arkansas, Mississippi and Tennessee, with more heavy rains and damaging winds in the mix.
Hundreds of Kentucky roads were impassable because of floodwaters, downed trees or mud and rock slides.
Downtown Hopkinsville, Kentucky, reopened in the morning after floodwaters from the Little River receded, giving a much-needed reprieve, but still more rainfall was on its way on Saturday and Sunday, Mayor James R Knight Jr said.
"We got a little rain, but most of it went north of us," Knight said. "Thank goodness on that. Gave us a little break."
In north-central Kentucky, emergency officials ordered a mandatory evacuation for Falmouth, a town of 2000 people in a bend of the rising Licking River. The warnings were similar to catastrophic flooding nearly 30 years ago when the river reached a record 15 metres, resulting in five deaths and 1000 homes destroyed.
Since Wednesday more than a 30.5cm has fallen in parts of Kentucky, and more than 20cm in parts of Arkansas and Missouri, forecasters said.
The state's emergency management office reported damage in 22 counties from tornadoes, wind, hail and flash flooding.
